Achieving ultra-broadband and ultra-low-frequency surface wave bandgaps in seismic metamaterials through topology optimization

Achieving broadband low-frequency surface wave bandgaps is technically challenging, which calls for a systematic design paradigm instead of intuitive approaches. In this study, we use topology optimization to design seismic metamaterials (SMMs) for achieving maximum surface wave bandgaps in the typical frequency range of seismic waves (1 ∼ 20 Hz) which might cause strongly destructive effects to surrounding buildings/structures. The proposed unified inverse-design scheme leads to a series of SMMs, which offer broadband low-frequency surface wave energy insulation. Typically, the lower-edge frequency of the bandgap can reach as low as 1.6 Hz, alongside a 10.3 Hz bandwidth (a relative bandwidth of around 150%). Overall, most optimized structures share similar topological features: slim connections and large masses, which can enhance the local resonance mode. Single pillared barrier is shown to exhibit three typical modes. As a result, multiple pillars (within one unit cell) are necessary for the higher-order bandgaps, and the number of pillars gradually increases with the targeted bandgap order. Frequency- and time-domain response analyses verify that the optimized SMMs can reduce the vibration amplitude over the ground surface within the designed bandgaps. At last, SMMs are customized to cope with realistic seismic signals by completely covering the dominant frequency region.